Novel mechanism of a charge density wave in a transition metal dichalcogenide

The charge density wave (CDW) is usually associated with Fermi surfaces nesting. We here report a new CDW mechanism discovered in a 2H-structured transition metal dichalcogenide, where the two essential ingredients of the CDW are realized in very anomalous ways due to the strong-coupling nature of the electronic structure. Namely, the CDW gap is only partially open, and charge density wave vector match is fulfilled through participation of states of the large Fermi patch, while the straight Fermi surface sections have secondary or negligible contributions.     

Charge density waves in layered compounds

The metallic layered compounds of the transition metal dichalcogenide type show unusual deviations from simple metallic behavior. These deviations are due to Charge Density Wave instabilities that are driven by the Fermi surface. The Charge Density Wave is a coupled periodic distortion of the conduction electron density and the crystal lattice. The effects of the CDW on the physical properties are qualitatively discussed. The basic driving forces of the CDW are most likely responsible for structural changes in a wide variety of materials, such as high temperature superconductors and long period superlattice alloys.     

Charge-density-wave partial gap opening in quasi-2D KMo6O17 purple bronze studied by angle resolved photoemission spectroscopy

Low dimensional (LD) metallic oxides have been a subject of continuous interest in the last two decades, mainly due to the electronic instabilities that they present at low temperatures. In particular, charge density waves (CDW) instabilities associated with a strong electron-phonon interaction have been found in Molybdenum metallic oxides such as KMo₆O₁₇ purple bronze. We report an angle resolved photoemission (ARPES) study from room temperature (RT) to T ∼40 K well below the Peierls transition temperature for this material, with CDW transition temperature T_CDW ∼120 K. We have focused on photoemission spectra along ΓM high symmetry direction as well as photoemission measurements were taken as a function of temperature at one representative k_F point in the Brillouin zone in order to look for the characteristic gap opening after the phase transition. We found out a pseudogap opening and a decrease in the density of states near the Fermi energy, E_F, consistent with the partial removal of the nested portions of the Fermi surface (FS) at temperature below the CDW transition. In order to elucidate possible Fermi liquid (FL) or non-Fermi liquid (NFL) behaviour we have compared the ARPES data with that one reported on quasi-1D K_0.3MoO₃ blue bronze.     

Indication of charge-density-wave formation in Bi(111)

Photoemission spectroscopy of Bi(111) reveals a small hexagonal two-dimensional Fermi surface (FS) associated with an electron band centered in the surface Brillouin zone. Along the hexagon the Fermi momentum k(F) ranges from 0.053 to 0.061 A(-1). Temperature dependent valence band spectra show an anisotropic energy gap Delta near the Fermi level. We find a transition temperature of about 75 K. At 11 K, the gap is Delta=4 meV at the corner and Delta=7.5 meV at the side of the hexagon. Arguments based on susceptibility chi(--> q) calculations of a hexagonal FS are used to discuss an incommensurate charge-density-wave (CDW) formation associated with a q(CDW)=0.106 A(-1).     

Reconstruction of the Fermi surface in the pseudogap state of cuprates

Reconstruction of the Fermi surface of high-temperature superconducting cuprates in the pseudogap state is analyzed within a nearly exactly solvable model of the pseudogap state, induced by short-range order fluctuations of the antiferromagnetic (AFM), spin-density wave (SDW), or a similar charge-density wave (CDW) order parameter, competing with the superconductivity. We explicitly demonstrate the evolution from “Fermi arcs” (on the “large” Fermi surface) observed in the ARPES experiments at relatively high temperatures (when both the amplitude and phase of the density waves fluctuate randomly) towards the formation of typical “small” electron and hole “pockets,” which are apparently observed in the de Haas-van Alphen and Hall resistance oscillation experiments at low temperatures (when only the phase of the density waves fluctuate and the correlation length of the short-range order is large enough). A qualitative criterion for the quantum oscillations in high magnetic fields to be observable in the pseudogap state is formulated in terms of the cyclotron frequency, the correlation length of fluctuations, and the Fermi velocity. The text was submitted by the authors in English.     

Angular studies of the magnetoresistance in the density wave state of the quasi-two-dimensional purple bronze KMo<Subscript>6</Subscript>O<Subscript>17</Subscript>

The purple molybdenum bronze KMo₆O₁₇ is a quasi-two-dimensional compound which shows a Peierls transition towards a commensurate metallic charge density wave (CDW) state. High magnetic field measurements have revealed several transitions at low temperature and have provided an unusual phase diagram “temperature-magnetic field”. Angular studies of the interlayer magnetoresistance are now reported. The results suggest that the orbital coupling of the magnetic field to the CDW is the most likely mechanism for the field induced transitions. The angular dependence of the magnetoresistance is discussed on the basis of a warped quasi-cylindrical Fermi surface and provides information on the geometry of the Fermi surface in the low temperature density wave state.     

Charge-density waves and superlattices in the metallic layered transition metal dichalcogenides

The d1 layer metals TaS 2 , TaSe 2 , NbSe 2 , in all their various polytypic modifications, acquire, below some appropriate temperature, phase conditions that their electromagnetic properties have previously revealed as 'anomalous'. Our present electron-microscopic studies indicate that this anomalous behaviour usually included the adoption, at some stage, of a superlattice. The size of superlattice adopted often is forecast in the pattern of satellite spotting and strong diffuse scattering found above the transition. Our conclusions are that charge-density waves and their concomitant periodic structural distortions occur in all these 4d 1 /5d 1 dichalcogenides. We have related the observed periodicities of these CDW states to the theoretical form of the parent Fermi surfaces. Particularly for the 1T octahedrally coordinated polytypes the Fermi surface is very simple and markedly two-dimensional in character, with large near-parallel walls. Such a situation is known theoretically to favour the formation of charge and spin-density waves. When they first appear, the CDWs in the 1T (and 4Hb) polytypes are incommensurate with the lattice. This condition produes a fair amount of gapping in the density of states at the Fermi level. For the simplest case of 1T-TaSe 2 , the room temperature superlattice is realized when this existing CDW rotates into an orientation for which it then become commensurate. At this first-order transition the Fermi surface energy gapping increases beyond that generated by the incommensurate CDW, as is clearly evident in the electromagnetic properties. For the trigonal prismatically coordinated polytypes, CDW formation is withheld to low temperatures, probably because of the more complex band structures. This CDW state (in the cases measured) would seem at once commensurate, even though the transition is, from a wide variety of experiments, apparently second order. A wide range of doped and intercalated materials have been used to substantiate the presence of CDWs in these compounds, and to clarify the effect that their occurrence has on the physical properties. The observations further demonstrate the distinctiveness of the transition metal dichalcogenide layer compounds, and of the group VA metals in particular.     

Charge-density waves in self-assembled halogen-bridged metal chains

Self-assembled growth of an ordered layer of Pt-Br-Pt chains on a Pt(110) surface is demonstrated. Upon slight doping with excess bromine, charge-density wave (CDW) domains separated by well-localized solutions are observed in the Br/Pt layer by scanning tunneling microscopy. Depending on annealing and adatom concentration, a global, long-range-ordered CDW ground state can be established. Angle-resolved UV photoemission data reveal the corresponding Fermi surface and its removal upon the Peierls transition. The CDW phase is stable to well above room temperature.     

Spectral properties of incommensurate charge-density wave systems

The concept of frustrated phase separation is applied to investigate its consequences for the electronic structure of the high T _c cuprates. The resulting incommensurate charge density wave (CDW) scattering is most effective in creating local gaps in k-space when the scattering vector connects states with equal energy. Starting from an open Fermi surface we find that the resulting CDW is oriented along the (10)- and (or) (01)-direction which allows for a purely one-dimensional or a two-dimensional “eggbox type” charge modulation. In both cases the van Hove singularities are substantially enhanced, and the spectral weight of Fermi surface states near the M-points, tends to be suppressed. Remarkably, a leading edge gap arises near these points, which, in the eggbox case, leaves finite arcs of the Fermi surface gapless. We discuss our results with repect to possible consequences for photoemission experiments. Received 14 June 1999     

Electron-lattice interaction and the CDW state of 1T-TiSe2

The electronic band structure in the CDW state (superlattice structure) of 1T-TiSe₂ is calculated on the basis of the band-type Jahn-Teller model by extending our theory of lattice instability in the normal phase. A strong coupling between the hole-band (Se p states) around the Λ point and the electron-bands (Ti d states) around the Λ points is caused by the electron-lattice interaction. Reflecting such a strong coupling remarkable changes appear in the dispersion curves near the Fermi energy and the largest CDW gap is obtained to be 0.2 eV. We have also calculated a change of the density of states near the Fermi energy due to the superlattice formation. The result is consistent with that observed by angle-integrated photoemmision by Margaritondo et al. It is also shown that the magnitude of the lattice distortion observed at low temperatures can be explained in a way consistent with the lattice dynamics in the normal phase.     

Scanning tunnelling microscopy of charge-density waves in transition metal chalcogenides

We have used scanning tunnelling microscopes (STMs) operating at liquid helium and liquid nitrogen temperatures to image the charge-density waves (CDWs) in transition metal chalcogenides. The layer structure dichalcogenides TaSe₂, TaS₂, NbSe₂, VSe₂, TiSe₂ and TiS₂ have been studied including representative polytype phases such as 1T, 2H and 4Hb. Experimental results are presented for the complete range of CDW amplitudes and structures observed in these materials. In most cases both the CDW and the surface atomic structure have been simultaneously imaged. Results on the trichalcogenide NbSe₃ are also included.

The formation of the CDW along with the associated periodic lattice distortion gaps the Fermi surface (FS) and modifies the local density-of-states (LDOS) detected by the tunnelling process. The tunnelling microscopes have been operated mostly in the constant current mode which maps the LDOS at the position of the tunnelling tip. The relative amplitudes and profiles of the CDW superlattice and the atomic lattice have been measured and confirm on an atomic scale the CDW structures predicted by X-ray, electron and neutron diffraction. The absolute STM deflections are larger than expected for the CDW induced modifications of the LDOS above the surface and possible enhancement mechanisms are reviewed.

In the 2H trigonal prismatic coordination phases the CDWs involve a relatively small charge transfer and the atomic structure dominates the STM images. In the 1T octahedral coordination phases the charge transfer is large and the CDW structure dominates the STM image with an anomalously large enhancement of the STM profile. Systematic comparison of the STM profiles with band structure and FS information is included.

In the case of the 4Hb mixed coordination phases at the lowest temperatures two nearly independent CDWs form in alternate sandwiches. STM studies on 4Hb crystals with both octahedral and trigonal prismatic surface sandwiches have been carried out. The STM scans detect the relative strengths of the two CDWs as well as the interactions between the two types of CDW structure.

The STM scans are also able to detect defects and domain structure in the CDW image. Several examples will be given demonstrating the potential of the STM to detect these local variations in LDOS on an atomic scale. In contrast to the layer structure crystals the linear chain compound NbSe₃ shows a complex surface atomic structure as well as the formation of two CDWs. The surface atomic structure is resolved in the STM scans and profiles have detected the presence of the CDW modulation at 77K and 4.2K. These results demonstrate the feasibility of detecting CDW structure in the presence of complex atomic structure and using materials where dynamical CDW effects can also be studied by STM.

The range of STM results presented here show that the STM scans are extremely sensitive to the detail of the CDW structure and its effect on the LDOS. Although much of this structure has been deduced from diffraction studies, the ability to examine the CDW structure on an atomic scale with the STM is new. The sensitivity of the STM method suggests potential applications to a wide range of electronic structures in materials.     

Revealing charge density wave formation in the LaTe2 system by angle resolved photoemission spectroscopy

We present the first direct study of charge density wave (CDW) formation in quasi-2D single layer LaTe2 using high-resolution angle resolved photoemission spectroscopy and low energy electron diffraction. CDW formation is driven by Fermi surface (FS) nesting, however, characterized by a surprisingly smaller gap ( approximately 50 meV) than seen in the double layer RTe2 compounds, extending over the entire FS. This establishes LaTe2 as the first reported semiconducting 2D CDW system where the CDW phase is FS nesting driven. In addition, the layer dependence of this phase in the tellurides and the possible transition from a stripe to a checkerboard phase is discussed.     

Magnetoresistance of a Two-Dimensional TbTe<Subscript>3</Subscript> Conductor in the Sliding Charge-Density Wave Regime

The magnetoresistance of a TbTe₃ two-dimensional conductor with a charge-density wave (CDW) has been measured in a wide temperature range and in magnetic fields of up to 17 T. At temperatures well below the Peierls transition temperature and in high magnetic fields, the magnetoresistance exhibits a linear dependence on the magnetic field caused by the scattering of normal charge carriers by “hot” spots of the Fermi surface. In the sliding CDW regime in low magnetic fields, a qualitative change in the magnetoresistance has been observed associated with the strong scattering of carriers by the sliding CDW.     

Charge-density-wave instabilities and quantum transport in the monophosphate tungsten bronzes with m = 5 alternate structure

Resistivity, thermoelectric power and magnetotransport measurements have been performed on single crystals of the quasi two-dimensional monophosphate tungsten bronzes (PO₂)₄(WO₃)_2m for m =5 with alternate structure, between 0.4 K and 500 K, in magnetic fields of up to 36 T. These compounds show one charge density instability (CDW) at 160 K and a possible second one at 30 K. Large positive magnetoresistance in the CDW state is observed. The anisotropic Shubnikov-de Haas and de Haas-van Alphen oscillations detected at low temperatures are attributed to the existence of small electron and hole pockets left by the CDW gap openings. Angular dependent magnetoresistance oscillations (AMRO) have been found at temperatures below 30 K. The results are discussed in terms of a weakly corrugated cylindrical Fermi surface. They are shown to be consistent with a change of the Fermi surface below 30 K. Received 23 November 1999 and Received in final form 23 March 2000     

Superconductivity at 5.2 K in ZrTe3 polycrystals and the effect of Cu and Ag intercalation

We report the occurrence of superconductivity in polycrystalline samples of ZrTe(3) at temperature 5.2 K at ambient pressure. The superconducting state coexists with the charge density wave (CDW) phase, which sets in at 63 K. The intercalation of Cu or Ag does not have any bearing on the superconducting transition temperature but suppresses the CDW state. The feature of a CDW anomaly in these compounds is clearly seen in the DC magnetization data. Resistivity data are analyzed in order to estimate the relative loss of carriers and reduction in the nested Fermi surface area upon CDW formation in ZrTe(3) and the intercalated compounds.     

Coexistence of gapless excitations and commensurate charge-density wave in the 2H transition metal dichalcogenides

An unexpected feature common to 2H transition metal dichalcogenides ( 2H TMDs) is revealed with a first-principles Wannier function analysis of the electronic structure of the prototype 2H TaSe2: The low-energy Ta "5d(z2)" bands governing the physics of a charge-density wave (CDW) is dominated by hopping between next-nearest neighbors. With this motivation we develop a minimal effective model for the CDW formation, in which the unusual form of the hopping leads to an approximate decoupling of the three sublattices. In the CDW phase one sublattice remains undistorted, leaving the bands associated with it ungapped everywhere in the Fermi surface, resolving the long-standing puzzle of the coexistence of gapless excitations and commensurate CDW in the 2H TMDs.     

Optical properties of the charge-density-wave polychalcogenide compounds R 2Te 5 (R=Nd, Sm and Gd)

We investigate the rare-earth polychalcogenide R₂Te₅ (R=Nd, Sm and Gd) charge-density-wave (CDW) compounds by optical reflectivity measurements. We obtain the optical conductivity through Kramers-Kronig transformation of the reflectivity spectra. From the real part of the optical conductivity we then extract the excitation energy of the CDW gap and estimate the fraction of the Fermi surface which is gapped by the formation of the CDW condensate. In analogy to previous findings on the related RTe_n (n=2 and 3) families, we establish the progressive closing of the CDW gap and the moderate enhancement of the metallic component upon chemically compressing the lattice.     

Dephasing of Andreev pairs entering a charge density wave

A Cooper pair from a s-wave superconductor (S) entering a conventional charge density wave (CDW) below the Peierls gap dephases on the Fermi wavelength while one particle states are localized on the CDW coherence length ξ_CDW. It is thus practically impossible to observe a Josephson current through a CDW. The paths following different sequences of impurities interfere destructively, due to the different electron and hole densities in the CDW. The same conclusion holds for averaging over the conduction channels in the ballistic system. We apply two microscopic approaches to this phenomenon: (i) a Blonder, Tinkham, Klapwijk (BTK) approach for a single highly transparent S-CDW interface; and (ii) the Hamiltonian approach for the Josephson effect in a clean CDW and a CDW with non magnetic disorder. The Josephson effect through a spin density wave (SDW) is limited by the coherence length ξ_SDW, not by the Fermi wave-length. A Josephson current through a SDW might be observed in a structure with contacts on a SDW separated by a distance ξ_SDW.